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Diego Maza Ozcoidi, Director of the department of Physics of the University of Navarra.

At the limits of mathematical formalism

Wed, 07 Oct 2020 09:00:00 +0000 Published in Navarra Newspaper
Diego Maza

As on other occasions I cannot deny a certain Degree of surprise at the Nobel Laureates in Physics 2020. In this case, I believe that the Academy itself lets us glimpse some of that same surprise. You will agree with me that it arouses some astonishment to read that someone is awarded for "the finding that the training of black holes is a robust prediction of the general theory of relativity". Surely it must be a robust prediction when it merits half of the award, instead of the quarter that corresponds to his peers.  

The latter have been awarded for discovering that a "supermassive object" conditions us from the center of our galaxy. The quotation marks are important. The Academy has been careful to assert that the center of our galaxy is inhabited by a supermassive object, which all the compelling evidence we have points to as a black hole of the kind that Penrose studied in the mid-1960's. However, if we know anything about these objects, it is how little we know about them. The reason is subtle and leads us to the "robust predictions" found by R. Penrose. In these objects, from which not even light is able to escape, the laws of physics become singular and the way in which nature behaves beyond them is a mystery, and where the very equations from which they are derived could be meaningless.

There are many elements that give rise to my surprise. Nothing to object to the Degree of refinement reached by astronomy to interpret the data of the center of our galaxy, much less of course to Penrose's singularity theorem that has triggered a huge amount of work in the world of cosmology. However, both facts are still burdened with a Degree significant amount of uncertainty and open questions. No doubt much progress has been made in finding that the mathematics are robust solutions to Einstein's equations, and that these are compatible with our observations of the Cosmos. Nevertheless, it never ceases to amaze me that the Academy must resort to the term "robust prediction" to justify its award. At least in recent years, I do not recall this Swedish institution using such an expression.

In any case, this year's award will almost certainly have a beneficial effect: many people will discover R. Penrose's knowledge dissemination works, some of which are written with masterful finesse. Whoever engages with them will travel almost unknowingly into the subtle - and often puzzling - predictions of mathematical formalism. Let us hope this is the case, for they are worthwhile.